Related papers: Monetary Risk Measures
In this paper we derive robust super- and subhedging dualities for contingent claims that can depend on several underlying assets. In addition to strict super- and subhedging, we also consider relaxed versions which, instead of eliminating…
Our paper contributes to the theory of conditional risk measures and conditional certainty equivalents. We adopt a random modular approach which proved to be effective in the study of modular convex analysis and conditional risk measures.…
In financial and actuarial research, distortion and Haezendonck-Goovaerts risk measures are attractive due to their strong properties. They have so far been treated separately. In this paper, following a suggestion by Goovaerts, Linders,…
To achieve robustness of risk across different assets, risk parity investing rules, a particular state of risk contributions, have grown in popularity over the previous few decades. To generalize the concept of risk contribution from the…
This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…
Within the context of capital adequacy, we study comonotonicity of risk measures in terms of the primitives of the theory: acceptance sets and eligible, or reference, assets. We show that comonotonicity cannot be characterized by the…
The aggregation of individual risks in large credit and insurance portfolios is guided by diversification and the law of large numbers, which formalizes the convergence of sample averages to their means. At the same time, regulatory capital…
Informally, a risk measure is said to be elicitable if there exists a suitable scoring function such that minimizing its expected value recovers the risk measure. In this paper, we analyze the elicitability properties of the class of return…
We consider monotone mean-variance (MMV) portfolio selection problems with a conic convex constraint under diffusion models, and their counterpart problems under mean-variance (MV) preferences. We obtain the precommitted optimal strategies…
This paper presents a systematic study of the notion of surplus invariance, which plays a natural and important role in the theory of risk measures and capital requirements. So far, this notion has been investigated in the setting of some…
We propose a definition of diversification as a binary relationship between financial portfolios. According to it, a convex linear combination of several risk positions with some weights is considered to be less risky than the probabilistic…
In this paper, we propose the multivariate range Value-at-Risk (MRVaR) and the multivariate range covariance (MRCov) as two risk measures and explore their desirable properties in risk management. In particular, we explain that such…
Scalar dynamic risk measures for univariate positions in continuous time are commonly represented as backward stochastic differential equations. In the multivariate setting, dynamic risk measures have been defined and studied as families of…
We extend techniques and learnings about the stochastic properties of nonlinear responses from finance to medicine, particularly oncology where it can inform dosing and intervention. We define antifragility. We propose uses of risk analysis…
Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first…
Under appropriate integrability conditions the risk measure of the sample measures for a law invariant risk measure converge almost surely to the risk measure of the sampled random variable. The results follow from general convergence…
Higher order risk measures are stochastic optimization problems by design, and for this reason they enjoy valuable properties in optimization under uncertainties. They nicely integrate with stochastic optimization problems, as has been…
Model uncertainty has been one prominent issue both in the theory of risk measures and in practice such as financial risk management and regulation. Motivated by this observation, in this paper, we take a new perspective to describe the…
We consider the problem of finding Pareto-optimal allocations of risk among finitely many agents. The associated individual risk measures are law invariant, but with respect to agent-dependent and potentially heterogeneous reference…
Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…